4.5.2.1 Number Base

Humans and computers are incompatible when they try to count.
While Humans use Decimal and Unary systems of counting, computers can only interpret Binary.
This is because computers can only process the presense or an absense of a signal, on or off, 1 or 0.

Characters

When writing down numbers, humans (while using base 10) have a choice of ten characters.
Computers only have a choice of two characters.

Below is a selection of different base systems and their characters.

Number System

Available Characters

Decimal (base 10)

0 1 2 3 4 5 6 7 8 9

Unary (base 1)

1

Binary (base 2)

0 1

Octal (base 8)

0 1 2 3 4 5 6 7

Hexadecimal (base 16)

0 1 2 3 4 5 6 7 8 9 A B C D E F

Conversions

Dec

Bin

Oct

Hex

Unary

0

0

0

0

1

1

1

1

1

2

10

2

2

11

3

11

3

3

111

4

100

4

4

1111

5

101

5

5

11111

6

110

6

6

111111

7

101

7

7

1111111

8

1000

10

8

11111111

9

1001

11

9

111111111

10

1010

12

A

1111111111

11

1011

13

B

11111111111

12

1100

14

C

111111111111

13

1101

15

D

1111111111111

14

1110

16

E

11111111111111

15

1111

17

F

111111111111111

16

10000

20

10

1111111111111111

To easily convert Decimal to Binary, attempt this methodology

Position

\(2^7\)

\(2^6\)

\(2^5\)

\(2^4\)

\(2^3\)

\(2^2\)

\(2^1\)

\(2^0\)

Decimal

128

64

32

16

8

4

2

1

12

No

No

No

No

Yes

Yes

No

No

Convert simply by subtracting powers of two until they fit.

Converting binary to hexadecimal is equally as easy.
Split the binary into groups of four and convert each 4 bits into a hex digit.